12y^2-5yz-2z^2=0

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Solution for 12y^2-5yz-2z^2=0 equation: 


Simplifying
12y2 + -5yz + -2z2 = 0

Reorder the terms:
-5yz + 12y2 + -2z2 = 0

Solving
-5yz + 12y2 + -2z2 = 0

Solving for variable 'y'.

Factor a trinomial.
(3y + -2z)(4y + z) = 0


Subproblem 1
Set the factor '(3y + -2z)' equal to zero and attempt to solve:

Simplifying
3y + -2z = 0

Solving
3y + -2z = 0

Move all terms containing y to the left, all other terms to the right.

Add '2z' to each side of the equation.
3y + -2z + 2z = 0 + 2z

Combine like terms: -2z + 2z = 0
3y + 0 = 0 + 2z
3y = 0 + 2z
Remove the zero:
3y = 2z

Divide each side by '3'.
y = 0.6666666667z

Simplifying
y = 0.6666666667z

Subproblem 2
Set the factor '(4y + z)' equal to zero and attempt to solve:

Simplifying
4y + z = 0

Solving
4y + z = 0

Move all terms containing y to the left, all other terms to the right.

Add '-1z' to each side of the equation.
4y + z + -1z = 0 + -1z

Combine like terms: z + -1z = 0
4y + 0 = 0 + -1z
4y = 0 + -1z
Remove the zero:
4y = -1z

Divide each side by '4'.
y = -0.25z

Simplifying
y = -0.25z
Solution
y = {0.6666666667z, -0.25z}

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